### List of Publications

**[1]** On the existence and regularity of fundamental domains with least boundary area,

J.
Differential Geom. 29 (1989), 623-663. PDF

**[2]** The isoperimetric inequality for a minimal surface with radially connected boundary,

Ann. Scuola Norm. Sup. Pisa (4), 17 (1990), 583-593. PDF

**[3]** Index, vision number, and stability of complete minimal surfaces,

Arch. Rat. Mech.
Anal. 109 (1990), 195-212. PDF

**[4]** On the analytic reflection of a minimal surface,

Pacific J. Math. 157 (1993), 29-35. PDF

**[5]** Isoperimetric inequalities on minimal submanifolds of space forms (with R. Gulliver),

Manuscripta Math. 77 (1992), 169-189. PDF

**[6]** The sharp isoperimetric inequality for minimal surfaces with radially connected
boundary in hyperbolic

space (with R. Gulliver), Inventiones Math. 109 (1992), 495-503. PDF

**[7]** Sharp isoperimetric inequalities for stationary varifolds and area minimizing flat chains mod k,

Kodai Math. J. 19 (1996), 177-190.
PDF

**[8]** Every stationary polyhedral set in R^n is area minimizing under diffeomorphisms,

Pacific J. Math. 175 (1996), 439-446.
PDF

**[9]** On the existence of higher dimensional Enneper's surface,

Comment. Math. Helvetici
71 (1996), 556-569.
PDF

**[10]** The isoenergy inequality for a harmonic map,

Houston J. Math. 24 (1998), 649-654.
PDF

**[11]** Nonexistence of certain complete minimal surfaces with planar ends (with M.
Soret),

Comment. Math. Helvetici 75 (2000), 189-199.
PDF

**[12]** The isoperimetric inequality for minimal surfaces in a Riemannian manifold,

J. reine angewandte Math. 506 (1999), 205-214.
PDF

**[13]** Sufficient conditions for constant mean curvature surfaces to be round,

Math. Ann.
323 (2002), 143-156. PDF

**[14]** Embedded minimal surfaces and total curvature of curves in a manifold (with R. Gulliver),

Math. Res. Letters 10 (2003), 343-362.
PDF

**[15]** Relative isoperimetric inequality for domains outside a convex set,

Archives
Inequalities Appl. 1 (2003), 241-250.
PDF

**[16]** Isoperimetric Inequalities of Minimal Submanifolds, Global Theory of Minimal Surfaces,

Clay Math. Proceedings 2 (2005), 325-369.
PDF
Streaming Video of my MSRI Lecture

**[17]** The relative isoperimetric inequality in Cartan-Hadamard 3-manifolds (with M. Ritore),

J. reine angewandte Math. 605 (2007), 179-191.
PDF

**[18]** The double cover relative to a convex set and the relative isoperimetric inequality,

J. Aust. Math. Soc. 80 (2006), 375-382.
PDF

**[19]** Total Positive curvature of hypersurfaces with convex boundary (with M. Ghomi and M. Ritore),

J. Differential Geom. 72 (2006), 129-147. PDF

**[20]** The relative isoperimetric inequality outside a convex domain in R^n (with M. Ghomi and M. Ritore),

Calc. Var. PDE. 29 (2007), 421-429. PDF

**[21]** First eigenvalue of symmetric minimal surfaces in S^3 (with M. Soret),

Indiana Univ. Math. J. 58 (2009), 269-282. PDF

**[22]** Capillary surfaces in a convex cone (with S.-H. Park), Math. Zeitschrift 267 (2011), 875-886. PDF

**[23]** Higher dimensional minimal submanifolds generalizing the catenoid and helicoid (with J. Hoppe),

Tohoku Math. J. 65 (2013), 43-55. PDF

**[24]** Density of a minimal submanifold and total curvature of its boundary (with R. Gulliver), Comm. Anal. Geom.

25 (2017), 545-556. PDF

**[25]** Noncommutative minimal surfaces (with J. Arnlind and J. Hoppe), Lett. Math. Phys. 106 (2016), 1109-1129. PDF LMP

**[26]** New minimal surfaces in S^3 desingularizing the Clifford tori (with M. Soret), Math. Ann. 364 (2016), 763-776. PDF

**[27]** Classical mechanics of minimal tori in S^3 (with J. Arnlind and J. Hoppe), preprint(arXiv:1307.2255).
PDF

**[28]** Stable capillary hypersurfaces in a wedge (with M. Koiso), Pacific J. Math. 280 (2016), 1-15. PDF

**[29]** On the area of minimal surfaces in a slab (with B. Daniel), Int. Math. Res. Notices 2016 (2016), 7201-7211.
PDF

**[30]** Mean curvature in manifolds with Ricci curvature bounded from below (with A. Fraser), preprint(arXiv:1605.06602).

to appear in Comment. Math. Helvetici PDF

**[31]** Higher dimensional Schwarz's surfaces and Scherk's surfaces (with J. Hoppe), preprint(arXiv:1607.07153). PDF

**[32]** Characterizing the harmonic manifolds by the eigenfunctions of the Laplacian (with S. Kim and J. Park),

preprint(arXiv:1707.05098). PDF

**[33]** Some minimal submanifolds generalizing the Clifford torus (with J. Hoppe), preprint(arxiv:1708.03430). PDF

#### Survey Papers

**[S1]** The History of the Plateau Problem,

Proceedings of Workshop in Pure Mathematics,
12 (1992), 69-90.
PDF

**[S2]** Characterizing the sphere in terms of volume, area, eigenvalues, and energy,

Proceedings of Workshop in Pure Mathematics, 17 (1997), 5-17.
PDF

**[S3]** The isoperimetric inequality of a minimal surface,

Proceedings of the Second
International Workshop on Differential Geometry, 2 (1998), 55-66. PDF

**[S4]** In search of nonexistent minimal surfaces,

Trends in Mathematics, 1 (1998), 183-187.
PDF

**[S5]** Ray preserving metrics and applications,

Proceedings of the Sixth
International Workshop on Differential Geometry, 6 (2002), 61-72. PDF

**[S6]** Minimal surfaces in S^3 and Yau's conjecture,

Proceedings of the 10th
International Workshop on Differential Geometry, 10(2005), 183-188. PDF

**[S7]** Radial viewpoint on minimal surfaces, Surveys in Geometric Analysis and Relativity, 59-72,

Advanced Lectures in Mathematics, International Press. PDF